My '95 Honda Accord when at a stoplight sometimes the brake drops and it starts inching forward. I have to release and depress the brake again to get it to stop again. I have had this happen on two occasions both near the end of longer trips. Any idea what needs repairing?

First, I would make sure the master cylinder is good and that the master cylinder reservoir is filled to the MAX line with brake fluid. Second, I would make sure the calipers and wheel cylinders are not leaking. Third, I would check the thickness of pads and shoes. Fourth, I would change the brake fluid, which is supposed to be done every two years. Fifth, I would take a flare wrench and ensure all brake line connections are tight.

My guess is that if you flushed your brake system the problem would be solved.

Have you tried bleeding the brakes? Sounds like you have air bubbles in your brake system

It's more serious than air in the lines (I am assuming that you have brake fluid in the reservoir). Air in the lines causes a spongy feeling but you don't loose the brakes as you describe.

Definitely a master cylinder problem. No doubts.
I would make an appointment to your reputable service station, get a quote to fix and get it repaired. An aftermarket master cylinder should cost about $100-$150.